The price of diesel is increased by 26%. A person wants to increase his expenditure by 15% only. By what percentage, correct to one decimal place, should he decrease his consumption?

Solution(By Examveda Team)

Given:
Percentage increase in the price of diesel = 26%
Percentage increase in total expenditure = 15%
Concept used:
P × C = E
Where P is Price, C is Consumption and E is Expenditure
Calculation:
Let initial price be P₁, consumption be C₁, and expenditure be E₁
P₁ × C₁ = E₁
⇒ $${{\text{C}}_1} = \frac{{{{\text{E}}_1}}}{{{{\text{P}}_1}}}$$
Let new price be P₂, new quantity consumed be C₂, and new expenditure be E₂
P₂ = P₁ + 26% of P₁
⇒ P₂ = 1.26P₁
E₂ = E₁ + 15% of E₁
⇒ E₂= 1.15E₁
As, P₂ × C₂ = E₂
⇒ 1.26P₁ × C₂ = 1.15E₁
⇒ C₂ = $$\frac{{{\text{1}}{\text{.15}}{{\text{E}}_1}}}{{{\text{1}}{\text{.26}}{{\text{P}}_1}}}$$
⇒ C₂ = 0.9126 × $$\frac{{{{\text{E}}_1}}}{{{{\text{P}}_1}}}$$
⇒ C₂ = 0.9126C₁
Decrease in consumption = C₁ - C₂
⇒ Decrease in consumption = C₁ - 0.9126C₁ = 0.0874C₁
Percentage decrease in consumption = $$\frac{{{\text{Decrease in consumption}}}}{{{\text{Initial consumption}}}} \times 100$$
⇒ Percentage decrease in consumption = $$\frac{{0.0874{{\text{C}}_1}}}{{{{\text{C}}_1}}} \times 100$$
∴ The percentage decrease in consumption is 8.7% (correct to 1 decimal place)